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    Anomalies in the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae
    (Elsevier, 2010) N/A; Department of Physics; Tuğrul, Murat; Kabakçıoğlu, Alkan; N/A; Faculty Member; Department of Physics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 49854
    We investigate the structural and dynamical properties of the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae and compare it with two "unbiased" ensembles: one obtained by reshuffling the edges and the other generated by mimicking the transcriptional regulation mechanism within the cell. Both ensembles reproduce the degree distributions (the first-by construction-exactly and the second approximately), degree-degree correlations and the k-core structure observed in Yeast. An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a collective organization which is achieved by subtle modifications in the network's degree distributions. We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions. We find that the Yeast's core network has a qualitatively different behavior, accommodating on average multiple attractors unlike typical members of both reference ensembles which converge to a single dominant attractor. Finally, we investigate the robustness of the networks and find that the stability depends strongly on the used function class. The robustness measure is squeezed into a narrower band around the order-chaos boundary when Boolean inputs are required to be nonredundant on each node. However, the difference between the reference models and the Yeast's core is marginal, suggesting that the dynamically stable network elements are located mostly on the peripherals of the regulatory network. Consistently, the statistically significant three-node motifs in the dynamical core of Yeast turn out to be different from and less stable than those found in the full transcriptional regulatory network.
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    Mathematical modeling of Behçet's disease: a dynamical systems approach
    (World Scientific Publ Co Pte Ltd, 2015) Gül, Ahmet; N/A; N/A; Department of Chemical and Biological Engineering; Department of Electrical and Electronics Engineering; Erdem, Cemal; Bozkurt, Yasemin; Erman, Burak; Demir, Alper; Master Student; PhD Student; Faculty Member; Faculty Member; Department of Chemical and Biological Engineering; Department of Electrical and Electronics Engineering; N/A; Graduate School of Sciences and Engineering; College of Engineering; College of Engineering; N/A; N/A; 179997; 3756
    Behcet's Disease (BD) is a multi-systemic, auto-inflammatory disorder that is characterized by recurrent episodes of inflammatory manifestations affecting skin, mucosa, eyes, blood vessels, joints and several other organs. BD is classified as a multifactorial disease with an important contribution of genetics. Genetic studies suggest that there is a strong association of BD with a Class I major histocompatibility complex antigen, named HLA-B*51, along with several other weaker associations with genes encoding proteins involved in inflammation. However, pathogenic mechanisms associated with these genetic variations and their interactions with the environment have not been elucidated yet. In this paper, we present a mathematical model for BD based on a dynamical systems perspective that captures especially the relapsing nature of the disease. We propose a disease progression mechanism and construct a model, in the form of coupled ordinary differential equations (ODEs), which reveals the occurrence pattern of the disease in the population. According to our model, the disease has three distinct modes describing different phenotypes of people carrying HLA-B*51 tissue antigen, namely, the Healthy Carrier, the Potential Patient and the Active Patient. We herein present an exemplary mathematical model for BD, for the first time in the literature, that concisely captures the actions of many cell types together with genetic and environmental effects. The proposed model provides insight into this complex inflammatory disease which may lead to identification of new tools for its treatment and prevention.